Massive And Massless Gauge Fields Formed by Flat Connections

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• 作者：İbrahim Şener ; Nurettin Karagöz ; Cenap Özel
• 关键词：Massive and massless gauge fields ; Holomorphic principal bundle ; Kähler potential ; Flat connection ; Mass matrix ; Abelian and nonabelian gauge group ; Topological charge ; Chern classes
• 刊名：International Journal of Theoretical Physics
• 出版年：2016
• 出版时间：January 2016
• 年：2016
• 卷：55
• 期：1
• 页码：17-40
• 全文大小：356 KB
• 参考文献：1.Chern, S.S.: Complex Manifolds Without Potential Theory. Springer Verlag (1995)
  2.Donaldson, S.K., Kronheimer, P.B.: The Geometry Of Four Manifolds. Oxford University Press (1990)
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  12.Moroianu, A.: Lectures on Kähler Geometry. Cambridge University Press (2007)
  13.Popov, A.D.: Holomorphic Analogs Of Topological Gauge Theories (2000)
  14.Streater, R.F.: Generalized Goldstone Theorem (1965)
  
• 作者单位：İbrahim Şener (1)
  Nurettin Karagöz (2)
  Cenap Özel (3)
  
  1. Department of Physics, Institute of Natural and Applied Sciences, Abant İzzet Baysal University, P. B. 14820 Gölköy Kampüsü, Merkez, Bolu, Turkey
  2. Department of Physics, Faculty of Science and Art, Abant İzzet Baysal University, P. B. 14820, Gölköy Kampüsü, Bolu, Turkey
  3. Department of Physics, Faculty of Science, Dokuz Eylül University, P. B. 35370 Tınaztepe Kampüsü, Buca - İzmir, Turkey
  
• 刊物类别：Physics and Astronomy
• 刊物主题：Physics
  Physics
  Quantum Physics
  Elementary Particles and Quantum Field Theory
  Mathematical and Computational Physics
  
• 出版者：Springer Netherlands
• ISSN：1572-9575

文摘

The Yang - Mills type massive and massless gauge theories are interpreted in the geometrical frame of holomorphic principal bundles on a complex 2 - manifold. It is seen in this formalism that, the component (1,1) of the curvature of this connection appears because of flat connections generated by holomorphic structure although connection is flat. Thus it is possible to write a Lagrangian for a Yang - Mills theory including massive and massless gauge fields. However, the mass matrix of a massive gauge field on such a bundle isn’t nilpotent and this field is generated by a noncommutative flat connection on the same bundle, then the structure group of this bundle is non - Abelian complex Lie group. However, if the gauge field is massless, then this is generated by commutative flat connection, and so the structure group of the bundle is Abelian complex Lie group. Also one sees that the second Chern number or topological charge is proportional to the total volume of the base manifold for each massless and massive gauge theories and Abelian (massless) gauge theories are indeed the theories of the Kähler potential on the complex projective space \(\mathbb {C}P^{2}\). Keywords Massive and massless gauge fields Holomorphic principal bundle Kähler potential Flat connection Mass matrix Abelian and nonabelian gauge group Topological charge Chern classes